Moore Machine and Accepting States

A Moore machine is a type of finite-state machine that has a specific output associated with each state. It is defined by a set of states, an input alphabet, an output alphabet, a transition function, and an output function. The transition function determines the next state based on the current state and the input, while the output function determines the output based on the current state.

Accepting states, also known as final states, are states in a finite-state machine that indicate the completion of a valid sequence of inputs. When the machine reaches an accepting state, it signifies that the input sequence has been successfully processed.

Statement a) "Moore machine has no accepting states" is a correct statement. A Moore machine does not have explicit accepting states. Instead, the output of a Moore machine is solely determined by the current state. The machine does not require an additional mechanism, such as accepting states, to signify the completion of a valid sequence.

Explanation of the Correct Answer

To understand why the statement is correct, let's compare Moore machines with Mealy machines.

Moore Machine vs. Mealy Machine

A Mealy machine is another type of finite-state machine that also has a specific output associated with each transition. In contrast to a Moore machine, the output of a Mealy machine depends not only on the current state but also on the input.

Conversion between Mealy and Moore Machines

Statement c) "We can convert Mealy to Moore but not vice versa" is incorrect. Both Mealy machines and Moore machines can be converted into each other.

Conversion from Mealy to Moore: To convert a Mealy machine to a Moore machine, we need to create additional states in the Moore machine to represent the possible combinations of current state and input in the Mealy machine. The outputs in the Moore machine will be determined solely by the current state, just like in a regular Moore machine.

Conversion from Moore to Mealy: To convert a Moore machine to a Mealy machine, we need to modify the output function of the Moore machine to consider the inputs as well. We associate outputs with transitions instead of states, allowing the Mealy machine to have outputs that depend on both the current state and the input.

Conclusion

In summary, the correct statement is a) "Moore machine has no accepting states." Moore machines do not have explicit accepting states. Instead, the output is solely determined by the current state. Mealy machines, on the other hand, do have accepting states. The statement c) "We can convert Mealy to Moore but not vice versa" is incorrect, as both Mealy and Moore machines can be converted into each other.